A Correlation Analysis of Risk Attributes and Returns: Evidence from the Returns and Volatility of Chinese Convertible Bonds

Abstract

The risk-return matching theory has been widely verified in mainstream investment products such as stocks and ordinary bonds (see, e.g., Sharpe, 1964; Fama & French, 1993). However, with the emergence of hybrid financial instruments, their risk-return characteristics have gradually challenged the traditional theoretical framework, and convertible bonds are a typical example. This study takes China's convertible bond market as the research object to explore the applicability of the traditional risk-return theory in this segmented market. To systematically analyse the risk-return characteristics of convertible bonds, this study adopts a combination of qualitative and quantitative methods, including text analysis, case analysis, comparative analysis, index construction, and Index Model (IM) analysis. Equal-weighted indices are constructed for convertible bonds and stocks respectively. Key indicators such as return rate, volatility, and Sharpe ratio are calculated, and parameters like alpha (α) and beta (β) are measured using the IM model for in-depth research. The research results show that convertible bonds break the “low-risk, low-return” matching relationship in the traditional theory. From the perspective of absolute risk-return characteristics, convertible bonds have low-risk attributes. However, this low-risk attribute does not compromise expected returns. Compared with the stock index, the annualized return rate of the convertible bond index is 1.66 times that of the stock index. The IM model shows that the α value of the convertible bond index is 6.115%, reflecting significant excess returns independent of the stock index. In addition, after classifying convertible bonds according to the stock-bond ratio (conversion value / pure bond value), this study finds that the risk-return distribution among different types of convertible bonds still conforms to the traditional symmetry law. The theoretical significance of this study lies in supplementing the gap of the traditional risk-return theory in the research of segmented markets and providing a new case for the traditional financial theory. In practice, it provides a basis for asset allocation. At the same time, the study provides a quantitative reference for institutional investors to construct convertible bond investment portfolios, such as the equal-weighted index construction method and the application of the IM model.